{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:UYWJ4OQDJE7KFXO7XTPHTN732Y","short_pith_number":"pith:UYWJ4OQD","schema_version":"1.0","canonical_sha256":"a62c9e3a03493ea2dddfbcde79b7fbd61c3525ea8c5357238c0ba1c0ead33a1d","source":{"kind":"arxiv","id":"2507.21189","version":1},"attestation_state":"computed","paper":{"title":"Operator-Based Machine Intelligence: A Hilbert Space Framework for Spectral Learning and Symbolic Reasoning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andreas Lemos, Andrew Kiruluta, Priscilla Burity","submitted_at":"2025-07-27T18:52:10Z","abstract_excerpt":"Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed as sampling and computation in infinite dimensional Hilbert spaces, leveraging tools from functional analysis, signal processing, and spectral theory. We review foundational concepts such as Reproducing Kernel Hilbert Spaces (RKHS), spectral operator learning, and wavelet-domain representations. We present a rigorous mathematical formulation of learning in Hi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.21189","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-27T18:52:10Z","cross_cats_sorted":[],"title_canon_sha256":"d4b2aec18b607fab44b1fc6f9a2ca20d9b94bc2ae1d4b36e31417fc77cef3822","abstract_canon_sha256":"3c09be915fa57ae53e90c870825fa028c517f3baeacef9150dd994f5b883b42e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:44:54.093978Z","signature_b64":"jJ37FNwQBOA619oaNAiXvanDtwtnqZatEjsOePmk0UN5qPQNOjoH9h7HOi1gC9QkoLdk7e7skVDtvudAr7PDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a62c9e3a03493ea2dddfbcde79b7fbd61c3525ea8c5357238c0ba1c0ead33a1d","last_reissued_at":"2026-07-05T11:44:54.093542Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:44:54.093542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Operator-Based Machine Intelligence: A Hilbert Space Framework for Spectral Learning and Symbolic Reasoning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Andreas Lemos, Andrew Kiruluta, Priscilla Burity","submitted_at":"2025-07-27T18:52:10Z","abstract_excerpt":"Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed as sampling and computation in infinite dimensional Hilbert spaces, leveraging tools from functional analysis, signal processing, and spectral theory. We review foundational concepts such as Reproducing Kernel Hilbert Spaces (RKHS), spectral operator learning, and wavelet-domain representations. We present a rigorous mathematical formulation of learning in Hi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.21189","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.21189/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.21189","created_at":"2026-07-05T11:44:54.093600+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.21189v1","created_at":"2026-07-05T11:44:54.093600+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.21189","created_at":"2026-07-05T11:44:54.093600+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYWJ4OQDJE7K","created_at":"2026-07-05T11:44:54.093600+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYWJ4OQDJE7KFXO7","created_at":"2026-07-05T11:44:54.093600+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYWJ4OQD","created_at":"2026-07-05T11:44:54.093600+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y","json":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y.json","graph_json":"https://pith.science/api/pith-number/UYWJ4OQDJE7KFXO7XTPHTN732Y/graph.json","events_json":"https://pith.science/api/pith-number/UYWJ4OQDJE7KFXO7XTPHTN732Y/events.json","paper":"https://pith.science/paper/UYWJ4OQD"},"agent_actions":{"view_html":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y","download_json":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y.json","view_paper":"https://pith.science/paper/UYWJ4OQD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.21189&json=true","fetch_graph":"https://pith.science/api/pith-number/UYWJ4OQDJE7KFXO7XTPHTN732Y/graph.json","fetch_events":"https://pith.science/api/pith-number/UYWJ4OQDJE7KFXO7XTPHTN732Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y/action/storage_attestation","attest_author":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y/action/author_attestation","sign_citation":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y/action/citation_signature","submit_replication":"https://pith.science/pith/UYWJ4OQDJE7KFXO7XTPHTN732Y/action/replication_record"}},"created_at":"2026-07-05T11:44:54.093600+00:00","updated_at":"2026-07-05T11:44:54.093600+00:00"}